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arXiv · 2211.00518

Holographic study of $T\bar{T}$ like deformed HV QFTs: holographic entanglement entropy

Hyun-Sik Jeong·Wen-Bin Pan·Ya-Wen Sun·Yuan-Tai Wang
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Abstract

We study the $(d+2)$-dimensional Hyperscaling Violating (HV) geometries in the presence of both a finite temperature $T$ and a UV cutoff $r_c$. This gravitational system is conjectured to be dual to $T\bar{T}$ like deformed HV QFTs. We consider the representative quantum entanglement quantity in holography, i.e. the entanglement entropy $S(A)$, and perform a complete analysis in all possible parameter ranges of the hyperscaling violation exponent $\theta$ and the critical dynamical exponent $z$ to study the effect of the temperature and the cutoff. We find that the temperature has a universal effect independent of the parameters: it enhances $S(A)$ in the small cutoff limit, while it is irrelevant in the large cutoff limit. For the cutoff effect, we find that the cutoff monotonically suppresses $S(A)$ where its behavior depends on the parameter range. As an application of the finite temperature analysis, we study the first law of entanglement entropy, $S_{T}-S_{T=0}\sim\ell^{\lambda}$, in the small subsystem size $\ell$ limit. We find that $\lambda$ interpolates between $\lambda=1+z$ in the small cutoff and $\lambda=3$ in the large cutoff, independent of the parameter range. We also provide the analytic holographic result at $z=d-\theta$ and discuss its possibility of comparison with the field theoretic result.

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Hyun-Sik Jeong, Wen-Bin Pan, Ya-Wen Sun, Yuan-Tai Wang. 2022-11-01. Holographic study of $T\bar{T}$ like deformed HV QFTs: holographic entanglement entropy. https://doi.org/10.1007/jhep02(2023)018

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